Question

A tire company makes tires that have a normal distribution with a mean of 65,000 miles and a standard deviation of 3000 miles prior to needing replacement. A tire that wears out after reaching the top 4% of miles lasted before needing replacement is considered very well made. Find the lowest number of miles that a tire would have to last to be considered very well made.

A company sells pumpkin seeds. They advertise that they will offer you 100 pounds of free topsoil if it takes their pumpkins more than a certain number of days to grow to maturity. They wish to only have to give away free topsoil at most 4% of the time, and the number of days it takes their seeds to grow to maturity follows a normal distribution with a mean of 106 days and a standard deviation of 5 days. They wish to advertise a number in whole days. What number of days will they advertise?

Answer 1

Solution:- Given that mean = 6500, sd = 3000
P(X > x) = 0.04, for Z = 1.75

X = mean + Z*Sd = 6500 + (1.75*3000) = 11750

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Soltution: given that mean = 106, sd = 5

P(X <= x) = 0.04, for Z = -1.75

X = X = mean + Z*Sd = 106 - (1.75*5) = 97.25